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Bound states of atoms in a homogeneous magnetic field
Author(s) -
Vugalter Semjon
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310282
Subject(s) - homogeneous , eigenvalues and eigenvectors , mathematics , operator (biology) , magnetic field , essential spectrum , spectrum (functional analysis) , field (mathematics) , value (mathematics) , mathematical physics , mathematical analysis , pure mathematics , combinatorics , quantum mechanics , chemistry , physics , statistics , biochemistry , repressor , transcription factor , gene
We consider Schrödinger operators of atoms in a homogeneous magnetic field. We prove that for each fixed value of the pseudomomentum, the corresponding operator has an infinite number of eigenvalues. The asymptotic behaviour of the counting function is studied for values of spectral parameter near the bottom of the essential spectrum. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)